Integrate Varied Time with airSlate SignNow

Integrate varied time

i thought we should talk about what is all this tal business anyway which uh that kind of title comes from an engineer from uh national i believe bob peace and um seems to generate a lot of confusion and there seems there's two towels that we speak of right the first tau right is the time constant of a first order system right with exponential decay and that can be an rc network where a tau equals rc or it can be you know a cooling cup of coffee anything like that right and it's important to know what tau is because when that system dissipates its energy that energy should be dissipated in approximately five tau right why well if i substitute t for five tau right i have the tiles cancel e to the minus five is close to zero all right so when you are trying to look at the time domain response of any first order system you're you're going to be looking at that tau and if you're testing one of these circuits right the pulse width of your function generator has to be greater than 5 tau so that you can actually see the system charge and discharge all right and that's the towel that you would have seen from your circuit design course then there's the other towel the towel that is the dummy variable that when we're integrating an equation based on time yet that resulting equation is a function of time we cannot use um we can't integrate with respect to a variable that's in the limit all right and usually we run into this um in the time domain convolution integral right where we want a function of time we have two functions of time that go into the mathematical convolution integral and so we just have to switch to some kind of dummy variable and we call that tau because it's time right but it really could be any variable because in the end we integrate out and that upper limit converts this back to a function of t all right and if you try to read other books or go to the you know wikipedia everybody does this what thing and one approach would be to just kind of air quotes buckle down until you realize that there's two different things however what people who say things like that forget is that when you're first learning it's kind of hard and you think that every variable kind of means something and it and it does right but unfortunately for this integration variable it is just kind of a mathematical trick so that we can integrate for time and get a function of time all right so let's see though where we can uh an example where this kind of falls apart just kind of you know sucking it up if you will so let's have g of t equals the step function and h of t equals...